# Is it possible to have mass with zero volume?

As we had always studied that matter occupied space and has mass and our universe is made of matter so do that mean that there is no case where mass is present without volume .

• The modern definition of mass used by particle physicists has nothing to do with space at all. Mass is defined in terms of the square of a systems energy-momentum four vector. May 4 '19 at 17:06

You are mentioning three things, matter, mass and volume.

Now mass (as the comment says) is just the square of the energy four vector.

Now I think what confused you is this from wiki:

In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume.

So basically you are talking about ordinary matter, that is made up of atoms, and takes up volume, and does have mass.

Now you are asking whether something can have mass, without having volume. If you include elementary particles, then the answer is that you could define mass (the square of the energy four vector) as the rest mass of an elementary particle, and in that case:

1. elementary particles, with rest mass, defined as point particles, having no spatial extension (volume), do exist, like the electron, quark

I think it is not possible. Although we may not know the specific volume associated with an arbitrary mass, a zero-volume mass would imply a black-hole as its characteristic radius would be less than the Schwarzschild radius. However, as far as we know, all blackholes (densiest bodies) have a non-zero characteristic volume.

• that's an interesting argument, but it's probably dangerous to assume that general relativity applies in the usual way at the scale of elementary particles ;)
– Will
May 4 '19 at 21:23